Algebra 1 Intermediate

Standard Form Converter

Convert between standard form Ax + By = C and slope-intercept form y = mx + b. Instantly find the slope, x-intercept, and y-intercept — with full step-by-step algebraic work and a graph.

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Convert in both directions
Intercepts + graph included
Input
Enter A, B, C for Ax + By = C
A
x +
B
y =
C
Examples
Enter slope m and y-intercept b for y = mx + b
Slope (m)
x +
Y-intercept (b)
Examples
Result
Enter values above to see the converted equation, slope, intercepts, and more.
Step-by-Step Conversion
Graph
Standard Form: Ax + By = C
Ax + By = C

Standard form is a way to write a linear equation where A, B, and C are integers and A is positive.

Rules for standard form:

  • A, B, and C must be integers (whole numbers)
  • A must be greater than 0 (positive)
  • GCD(A, B, C) = 1 (no common factor — fully reduced)
  • No fractions or decimals in the coefficients
To find the x-intercept, set y = 0: x = C/A. To find the y-intercept, set x = 0: y = C/B.
When to Use Standard Form

Standard form might feel less intuitive than slope-intercept, but it's extremely useful in several situations.

  • Finding both intercepts quickly (set x=0 or y=0)
  • Solving systems of equations by elimination
  • Describing vertical lines (x = k) that slope-intercept can't
  • Working with integer coefficients in textbook problems
  • Graphing a line using just two intercept points
Standard form makes the elimination method for systems of equations especially clean — line up Ax + By = C terms and add or subtract to cancel a variable.
Related Calculators
Slope-Intercept Form
Graph and explore y = mx + b — slope, intercepts, and more.
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Point-Slope Form
Write a line equation from a point and slope — y − y₁ = m(x − x₁).
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X & Y Intercepts
Find where any linear equation crosses the x and y axes.
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